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RELAXING CONVERGENCE ASSUMPTIONS FOR CONTINUOUS
ADAPTIVE CONTROL
by
Mubarak Alharashani
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A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful llment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
August 2010
Copyright 2010 Mubarak Alharashani

Adaptive control convergence has been proved for long time by using slow switching schemes through separating the two successive switching events by a positive time interval (e.g., dwell-time, average dwell-time, hysteresis switching technique). This thesis addresses the inherent limitations of some logic-based switching among infinite (i.e. continuum) set of candidate controllers. In this thesis, we examine adaptive control convergence in the context of well-known hysteresis switching algorithm by relaxing the usual requirement that the hysteresis constant is strictly positive. Relaxing this constraint allows the adaptive controller to converge to a unique optimum in the case of an infinite (continuum) candidate controller set, provided that at least one controller in the controller set has the ability to satisfy adaptive control performance.

RELAXING CONVERGENCE ASSUMPTIONS FOR CONTINUOUS
ADAPTIVE CONTROL
by
Mubarak Alharashani
||||||||||||||||||||||||{
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful llment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
August 2010
Copyright 2010 Mubarak Alharashani